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On the distribution of V OTAW 's likelihood ratio criterion L for testing the bipolarity of a covariance matrix
Author(s) -
Consul P. C.
Publication year - 1968
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.19680360102
Subject(s) - mathematics , covariance matrix , likelihood ratio test , transformation (genetics) , expression (computer science) , statistics , covariance , distribution (mathematics) , function (biology) , series (stratigraphy) , matrix (chemical analysis) , mellin transform , likelihood function , maximum likelihood , combinatorics , mathematical analysis , laplace transform , biochemistry , chemistry , materials science , computer science , composite material , gene , programming language , evolutionary biology , paleontology , biology
In this paper the exact distribution function of Votaw's likelihood ratio criterion L has been obtained in the form of an infinite series by applying Mellin's transformation on the moments and then by using the asymptotic expansion for log Γ( x + h ). The author has actually calculated the values of the constants for some particular cases and has shown that the first four or five terms give a high degree of accuracy. An expression for the Integral probability of the distribution has also been obtained.